Question

An unknown gas effuses at one half the speed of oxygen. What is the molar mass of the unknown? It is either HBr or HI. Which gas is it?

Answer 1

Answer:

HI.

Explanation:

• Thomas Graham found that, at a constant  temperature and pressure the rates of effusion  of various gases are inversely proportional to  the square root of their masses.

Rate of effusion ∝ 1/√molar mass.

• (Rate of effusion of O₂) / (Rate of effusion of unknown gas) = (√molar mass of unknown gas) / (√molar mass of O₂).

• An unknown gas effuses at one half the speed of that of oxygen.

∵ Rate of effusion of unknown gas = 1/2 (Rate of effusion of O₂)

∴ (Rate of effusion of O₂) / (Rate of effusion of unknown gas) = 2.

Molar mass of O₂ = 32.0 g/mol.

∵ (Rate of effusion of O₂) / (Rate of effusion of unknown gas) = (√molar mass of unknown gas) / (√molar mass of O₂).

∴  2.0 = (√molar mass of unknown gas) / √32.0.

( √molar mass of unknown gas) = 2.0 x √32.0

By squaring the both sides:

∴ molar mass of unknown gas = (2.0 x √32.0)² = 128 g/mol.

∴ The molar mass of sulfur dioxide = 80.91 g/mol and the molar mass of HI = 127.911 g/mol.

So, the unknown gas is HI.